Combine the brown sugar, butter, and cinnamon in a small saucepan. Cook over low heat until the sugar dissolves.
Carefully add the rums and stir to combine. Simmer for 3 minutes.
Store sauce in a sealed container in the refrigerator until needed.
For the Grilled Pineapple:
Turn pineapple on it's side and slice into approximately 1/2-inch rounds.
Using a sharp knife, cut around the outside edge to remove the skin.
Use an apple corer {or sharp knife} to remove the core in each slice.
Place pineapple slices on a preheated grill and cook for 3 to 5 minutes on each side.
Place each pineapple slice in a bowl, top with vanilla {or coconut} ice cream and drizzle with sauce.
Garnish with toasted coconut, if desired.
Notes
If you do not want to use coconut rum, substitute a silver rum.
If you do not want to use rum at all, go to the grocery store and buy a jar of caramel sauce.
If you look closely you will notice that I burned the bottoms of my pineapple slices {I got distracted by the dog}. No worries, they still tasted great and had a slightly smokey flavor to them, lol
I did not brush the pineapple with oil before grilling and they did not stick.
No, I do not know if canned pineapple would work, I have only tried grilling fresh pineapple.